A homogenization method to model a stack of second generation High Temperature Superconducting tapes under AC applied transport current or magnetic field has been obtained. The idea is to find an anisotropic bulk equivalent for the stack such that the geometrical layout of the internal alternating structures of insulating, metallic, superconducting, and substrate layers is “washed” out while keeping the overall electromagnetic behavior of the original stack. We disregard assumptions upon the shape of the critical region and use a power law E–J relationship allowing for overcritical current densities to be considered. The method presented here allows for a computational speedup factor of up to 2 orders of magnitude when compared to full 2-D simulations taking into account the actual dimensions of the stacks without compromising accuracy.
REFERENCES
1.
S.
Terzieva
et al., “Transport and magnetization ac losses of ROEBEL assembled coated conductor cables: Measurements and calculations
,” Supercond. Sci. Technol.
23
, 014023
(2010
).2.
Z.
Jiang
et al., “AC loss measurements in pancake coils wound with 2G tapes and Roebel cable: Dependence on spacing between turns/strands
,” Supercond. Sci. Technol.
25
, 035002
(2012
).3.
V. M.
Rodriguez-Zermeno
et al., “Towards faster FEM simulation of thin film superconductors: A multiscale approach
,” IEEE Trans. Appl. Supercond.
21
, 3273
–3276
(2011
).4.
R.
Brambilla
, F.
Grilli
, D. N.
Nguyen
, L.
Martini
, and F.
Sirois
, “AC losses in thin superconductors: The integral equation method applied to stacks and windings
,” Supercond. Sci. Technol.
22
, 075018
(2009
).5.
J.
Clem
, “Field and current distributions and ac losses in a bifilar stack of superconducting strips
,” Phys. Rev. B
77
, 134506
(2008
).6.
J.
Šouc
, E.
Pardo
, M.
Vojenčiak
, and F.
Gömöry
, “Theoretical and experimental study of AC loss in high temperature superconductor single pancake coils
,” Supercond. Sci. Technol.
22
, 015006
(2009
).7.
M. D.
Ainslie
et al., “An improved FEM model for computing transport AC loss in coils made of RABiTS YBCO coated conductors for electric machines
,” Supercond. Sci. Technol.
24
, 045005
(2011
).8.
J. R.
Clem
, J. H.
Claassen
, and Y.
Mawatari
, “AC losses in a finite Z stack using an anisotropic homogeneous-medium approximation
,” Supercond. Sci. Technol.
20
, 1130
–1139
(2007
).9.
W.
Yuan
, A. M.
Campbell
, and T. A.
Coombs
, “A model for calculating the AC losses of second-generation high temperature superconductor pancake coils
,” Supercond. Sci. Technol.
22
, 075028
(2009
).10.
L.
Prigozhin
and V.
Sokolovsky
, “Computing AC losses in stacks of high-temperature superconducting tapes
,” Supercond. Sci. Technol.
24
, 075012
(2011
).11.
R.
Pecher
, M. D.
Mcculloch
, S. J.
Chapman
, and L.
Prigozhin
, “3D-modelling of bulk type-II superconductors using unconstrained H-formulation
,” in Proceedings of the EUCAS (2003
).12.
K.
Kajikawa
, T.
Hayashi
, R.
Yoshida
, M.
Iwakuma
, and K.
Funaki
, “Numerical evaluation of AC losses in HTS wires with 2D FEM formulated by self magnetic field
,” IEEE Trans. Appl. Supercond.
13
, 3630
–3633
(2003
).13.
Z.
Hong
, A. M.
Campbell
, and T. A.
Coombs
, “Numerical solution of critical state in superconductivity by finite element software
,” Supercond. Sci. Technol.
19
, 1246
–1252
(2006
).14.
R.
Brambilla
, F.
Grilli
, and L.
Martini
, “Development of an edge-element model for AC loss computation of high-temperature superconductors
,” Supercond. Sci. Technol.
20
, 16
–24
(2007
).15.
See www.comsol.com for COMSOL Multiphysics.
16.
D. N.
Nguyen
, S. P.
Ashworth
, J. O.
Willis
, F.
Sirois
, and F.
Grilli
, “A new finite-element method simulation model for computing AC loss in roll assisted biaxially textured substrate YBCO tapes
,” Supercond. Sci. Technol.
23
, 025001
(2010
).17.
V. M. R.
Zermeno
, F.
Grilli
, and F.
Sirois
, “A full 3D time-dependent electromagnetic model for Roebel cables
,” Supercond. Sci. Technol.
26
, 052001
(2013
).18.
See http://www.superpower-inc.com for SuperPower Inc.
19.
Y.
Kim
, C.
Hempstead
, and A.
Strnad
, “Magnetization and critical supercurrents
,” Phys. Rev.
129
, 528
–535
(1963
).20.
K. P.
Thakur
, A.
Raj
, E. H.
Brandt
, J.
Kvitkovic
, and S. V.
Pamidi
, “Frequency-dependent critical current and transport ac loss of superconductor strip and Roebel cable
,” Supercond. Sci. Technol.
24
, 065024
(2011
).21.
22.
J.
Lu
, E. S.
Choi
, and H. D.
Zhou
, “Physical properties of Hastelloy® C-276TM at cryogenic temperatures
,” J. Appl. Phys.
103
, 064908
(2008
).23.
V. M. R.
Zermeno
et al., “Simulation of an HTS synchronous superconducting generator
,” Phys. Proc.
36
, 786
–790
(2012
).24.
25.
A.
Bossavit
, Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements
(Academic Press
, 1997
), p. 352
.© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.
